Which of the following numbers is a factor of 155? ${2,5,7,9,10}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $155$ by each of our answer choices. $155 \div 2 = 77\text{ R }1$ $155 \div 5 = 31$ $155 \div 7 = 22\text{ R }1$ $155 \div 9 = 17\text{ R }2$ $155 \div 10 = 15\text{ R }5$ The only answer choice that divides into $155$ with no remainder is $5$ $ 31$ $5$ $155$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $155$ $155 = 5\times31 5 = 5$ Therefore the only factor of $155$ out of our choices is $5$. We can say that $155$ is divisible by $5$.